Question

Express Mail offers overnight delivery to customers. It is attempting to come to some conclusion on whether to expand its facilities. Currently its fixed costs are \(2 million per month, and its variable costs are \)2 per package. It charges \(12 per package and has a monthly volume of 2 million packages. If it expands, its fixed costs will rise by \)1 million and its variable costs will fall to $1.50 per package. Should it expand?

Short answer

Why or why not? Answer: No, Express Mail should not expand its facilities because the current profit and the profit after expansion are the same, indicating that there is no financial benefit from expanding the facilities.

Step-by-step solution

Calculate current profit

First, we need to calculate the profit for Express Mail with its current facilities. Profit is calculated as (Revenue - Costs), where Revenue = Price per package * Number of packages, Fixed costs = \(2 million, and Variable costs = \)2 per package. Revenue = \(12 per package * 2 million packages = \)24 million Variable costs = \(2 per package * 2 million packages = \)4 million Fixed costs = $2 million Current profit = Revenue - (Fixed costs + Variable costs) = \(24 million - (\)2 million + \(4 million) = \)18 million

Calculate profit after expansion

Now, we need to calculate the profit after expanding the facilities. After expansion, the fixed costs rise by \(1 million, and the variable costs fall to \)1.50 per package. New fixed costs = \(2 million + \)1 million = $3 million New variable costs = \(1.50 per package * 2 million packages = \)3 million Revenue remains the same as before, which is $24 million. Profit after expansion = Revenue - (New fixed costs + New variable costs) = \(24 million - (\)3 million + \(3 million) = \)18 million

Compare profits and decide

Now we have the current profit and the profit after expansion: Current profit = $18 million Profit after expansion = $18 million Since both the current profit and the profit after expansion are the same, there is no financial benefit from expanding the facilities. Therefore, based on this analysis, Express Mail should not expand its facilities.

Key concepts

Fixed and Variable Costs

When a business like Express Mail considers expanding, understanding fixed and variable costs is crucial. Fixed costs are expenses that do not change regardless of how much a company produces or sells. Think of them as the baseline operating costs, such as rent, salaries, and equipment leases. For Express Mail, this includes the mentioned \(2 million per month.

Variable costs, on the other hand, fluctuate with production volume. These costs include materials, labor, and other expenses directly tied to the number of units produced or services offered—like the \)2 per package that Express Mail spends.

A crucial aspect of managing these costs is understanding how they interact. For instance, Express Mail's decision to expand would increase its fixed costs to \(3 million but reduce variable costs to \)1.50 per package. This shift can have significant implications for profitability under different scenarios of demand and is essential to their decision-making process.

Profit Calculation

The essence of any business operation boils down to profit calculation, an indicator of financial health. To calculate profit, we subtract total costs from total revenue, with the formula: Profit = Revenue - (Fixed Costs + Variable Costs). For Express Mail, this involves determining both the current profit and the potential profit after expansion.

With a revenue of \(24 million from delivering 2 million packages at \)12 each, and costs comprising of both fixed and variable components, the calculation sheds light on the profitability before and after the proposed expansion. A key takeaway for students is to assess how changes in fixed and variable costs impact profit. Surprisingly, despite the changes in costs due to expanding facilities for Express Mail, the profit remained at $18 million, showing no apparent financial benefit from the expansion.

Economies of Scale

Another pivotal concept in business decisions is economies of scale. It refers to the cost advantage that arises with increased output of a product. As production grows, the cost per unit typically decreases, primarily because fixed costs are spread over a larger number of units. Variable costs also may decrease due to more efficient use of resources or bulk purchasing discounts.

In the context of Express Mail, by expanding and potentially increasing the volume of mail handled, one might expect to realize economies of scale. However, the exercise shows that even after the expansion, with fixed costs increasing and variable costs decreasing per package, the total profit doesn't change. This highlights an important lesson: economies of scale do not always lead to increased profit, especially if prices and total volume remain unchanged. Students should analyze both cost structures and market conditions to truly understand when economies of scale can be beneficial.